This invention relates generally to automatic belay apparatus and its use; and more particularly it concerns the provision of safe, easily used, simple and compact, fall protection/lowering apparatus which can be employed in many situations to save lives and also for recreational purposes.
There is a known phenomenon that when a rope is wrapped around a fixed cylinder an X tension is applied to one end of the rope, a reactive force less than X (we will call Y) will stop the rope from slipping. More wraps around the cylinder will reduce the required Y force necessary for equilibrium.
Once equilibrium is attained between X and Y, reducing Y force by some A amount will allow the rope to slip. The amount of reduction in Y is dependent upon, among other things, the elasticity of the rope, the number of wraps around the cylinder, the diameter of the cylinder, and the co-efficient of friction between the rope and the cylinder.
To belay in nautical terms, is to "make fast (a rope) by winding on a cleat or pin".
If one is climbing, to be belayed is to be protected (by a rope) from falling. This is accomplished by wrapping a rope around the belayer, or some other object, so as to reduce the Y tension when a climber falls, creating X tension. The governing equation depicting this phenomenon is: EQU X.sub.tension =.theta..sup.a FY.sub.tension
Where .theta..sup.a =Number of degrees, in radians, that the rope is in contact with a fixed cylinder
F=Coefficient of friction between the rope and the cylinder
a=Rope coefficient
Therefore, the greater number of wraps (radians), the lower Y is required for equilibrium.
And here is the paradox. If one wished Y to be minimal, multiple wraps are required; but, if one wishes to take up slack on the X rope when climbing by taking up Y tension, the weight of the rope X will be multiplied by the same factor (but in reverse) as when the climber falls which might make it impossible to take up slack, and hence a non-functional device. As one example:
For a wire rope, with 51/2 wraps around a 3" pipe (3.5 O.D.), EQU X=50# and Y=0.12#
Therefore, the amplification factor is 50#/0.12=400# Now, remove the 49# weight leaving a 1# rope and try to pull Y. Y=1#.times.400=400# to take up slack. This is not possible, or practicable.
Accordingly, there is need for improved apparatus to overcome the above problem so that slack can be automatically taken up while using the multiplying effect of multiple wraps; and there is need for apparatus which can be easily used for safe lowering of weights, as from great heights.